Find the values of the polynomial for the given values of the variable.
-x2-5x-6
x=-3
x=-2
I got 0 for the first one and 0 for the second. Am I figuring them wrong? (and that is an x squared, not 2x)
-(-3)^2 -5(-3)-6
-(9)+15-6=0
Thanks!
you are right in both cases
-x^2-5x-6
=-(x^2+5x+6)
=-(x+2)(x+3)
notice if this had been an equation equal to zero,
x=-2 and x=-3 would have been solutions.
That is why both values gave you a zero answer.
You are correct in your calculations. For the given polynomial -x^2 - 5x - 6, you substituted x = -3 and x = -2 to find the values of the polynomial. Let's go through the calculations you did:
For x = -3:
-(-3)^2 - 5(-3) - 6
-9 + 15 - 6 = 0
And for x = -2:
-(-2)^2 - 5(-2) - 6
-4 + 10 - 6 = 0
Therefore, for both values of x, you obtained 0 as the result. This means that both -3 and -2 are solutions to the polynomial equation. In fact, we can factor the polynomial as follows:
-x^2 - 5x - 6 = -(x + 2)(x + 3)
From the factored form, we can see that when x is equal to -2 or -3, the polynomial evaluates to 0. So, you correctly found the solutions to the polynomial equation. Well done!